Thermodynamics, Chaos, and Complexity

Classical thermodynamics is characterized by two laws: first,
the conservation of energy and secondly, the non-decrease of entropy
in closed systems isolated from their environment. Examples include
gas in a balloon, liquid cooling in a container, wood burning
in a stove. Since all such phenomena moved from states of low
to states of high entropy and were said to be irreversible, thermodynamics
seemed to point to an "arrow of time" contrary to classical
mechanics, for which all phenomena are reversible in time.

By the end of the nineteenth century, it had been shown that
classical thermodynamics could be reduced to classical mechanics
via statistical mechanics. To do so one treats solids, liquids
and gases as composed of atoms, and regards bulk properties such
as pressure, temperature and volume as arising from the motion
of atoms. Since the motion of atoms obeyed classical mechanics,
thermodynamic properties could be shown to be `epiphenomena,
i.e., rooted in the underlying atomic motion. The reduction of
classical thermodynamics also explained the apparent arrow of
time as resulting from a system going from a complex, highly organized
state, to a simple, disorganized state. Once again, fundamental
physics was without an arrow of time.

During the twentieth century, non-linear, non-equilibrium systems
were studied. These open systems exchange matter and/or energy
with their larger environment, and in doing so, they can move
from a less ordered to a more ordered state. The process decreases
their entropy without violating the Second Law, since the total
entropy of the system plus its environment increases in accordance
with the Second Law. This phenomena is frequently called "order
out of chaos" and such systems are called "dissipative
systems." Does this reintroduce an arrow of time? It does
phenomenologically, but whether it does so at a fundamental level
is still an open question, since the underlying laws governing
the atoms of these systems reflect temporal reversibility.

Recently there has been extensive study of systems obeying
classical physics (e.g.., mechanics, meteorology, hydrodynamics,
animal populations, etc.) and called chaotic, complex and self-organizing
systems. These systems display an incredible sensitivity to their
environment, epitomized in the famous "butterfly" effect
where a small perturbation in, say, Nairobi effects the weather
some weeks later in, say, Kyoto. Even in the simplest cases, chaotic
systems appear entirely random even though they are governed by
a deterministic equation. "Chaotic randomness"
is thus a combination of phenomenologically random data governed
by an entirely deterministic equation. On the one hand, it allows
us to increasingly bring into the deterministic framework of classical
science broad areas of phenomena which seemed to resist such inclusion.
On the other hand, it represents a limit to the complete testability
of the classical paradigm. This is because the practical limitations
on predictability means we cannot rule out the possibility that
certain macroscopic phenomena may in fact be genuinely random
(not in fact governed by a deterministic equation). Meanwhile,
chaos, self-organization and complexity theory help to explain
how biological complexity arose in conformity with thermodynamics,
and they give tacit support to the hope of some scholars that
nature at the macroscipic level may in fact be ontologically open.